Question

How do you convert $\dfrac{23.5}{100}$ into a decimal and percent?

Answer 1

We need to find the fraction form and percentage of the fraction $\dfrac{23.5}{100}$ . We can convert the fraction into decimal by changing the position of the decimal point. To compensate for that we have to multiply $\dfrac{1}{100}$. We multiply the fraction with 100 to find the percentage value.

Complete step by step solution:
For the given fraction $\dfrac{23.5}{100}$, we move the decimal to the left one position. The
decimal goes to the leftmost position.
We compensate the movement of the decimal by multiplying $\dfrac{1}{100}$ to the numerator and denominator of the main number $\dfrac{23.5}{100}$. The fraction $\dfrac{23.5}{100}$ is equal to $0.235$.
We explain the first two steps. The decimal starts from its actual position in $23.5$.
Now it crosses the number 3. The number changes from $23.5$ to $2.35$.
This means we have to multiply $\dfrac{1}{10}$. There is one more digit to cross.
So, $\dfrac{23.5}{100}$ becomes $\dfrac{23.5}{100}=\dfrac{2.35}{10}$.
Now in the second step the point goes to the leftmost position. The number again changes from $2.35$ to $0.235$. We again multiplied ${{10}^{-1}}$ for the decimal’s movement.
The final ratio is $\dfrac{23.5}{100}=\dfrac{.235}{1}=0.235$. The decimal is $0.235$.
We now try to find the percentage value of the fraction. We multiply the fraction with 100.
Therefore, $\dfrac{23.5}{100}\times 100=23.5$.
The decimal is $0.235$ and its percentage value is $23.5$.

Note: The value of the fraction is actually the unitary value of $23.5$ out of 100. Therefore, in percentage value we got $23.5$ as the percentage. Percentage deals with the ratio out of 100. The ratio value for both fraction and percentage is the same.